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• W4296124410 abstract "We present an a posteriori shock-capturing finite volume method algorithm called GP-MOOD that solves a compressible hyperbolic conservative system at high-order solution accuracy (e.g., third-, fifth-, and seventh-order) in multiple spatial dimensions. The GP-MOOD method combines two methodologies, the polynomial-free spatial reconstruction methods of GP (Gaussian Process) and the a posteriori detection algorithms of MOOD (Multidimensional Optimal Order Detection). The spatial approximation of our GP-MOOD method uses GP's unlimited spatial reconstruction that builds upon our previous studies on GP reported in Reyes et al. (2018) [20] and Reyes et al. (2019) [21]. This paper focuses on extending GP's flexible variability of spatial accuracy to an a posteriori detection formalism based on the MOOD approach. We show that GP's polynomial-free reconstruction provides a seamless pathway to the MOOD's order cascading formalism by utilizing GP's novel property of variable (2R+1)th-order spatial accuracy on a multidimensional GP stencil defined by the GP radius R, whose size is smaller than that of the standard polynomial MOOD methods. The resulting GP-MOOD method is a positivity-preserving method. We examine the numerical stability and accuracy of GP-MOOD on smooth and discontinuous flows in multiple spatial dimensions without resorting to any conventional, computationally expensive a priori nonlinear limiting mechanism to maintain numerical stability." @default.
• W4296124410 created "2022-09-17" @default.
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• W4296124410 date "2022-12-01" @default.
• W4296124410 modified "2023-10-18" @default.
• W4296124410 title "GP-MOOD: A positivity-preserving high-order finite volume method for hyperbolic conservation laws" @default.
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• W4296124410 doi "https://doi.org/10.1016/j.jcp.2022.111603" @default.
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